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<p id="mathjaxlink" class="pcenter"><a href="chap13_mj.html">[MathJax on]</a></p>
<p><a id="X85EE0CDD7D162BC7" name="X85EE0CDD7D162BC7"></a></p>
<div class="ChapSects"><a href="chap13.html#X85EE0CDD7D162BC7">13 <span class="Heading">Create wrapper hulls of a category</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap13.html#X7D03633A7D98026B">13.1 <span class="Heading">GAP categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X82BF68357D8889C4">13.1-1 IsWrapperCapCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X7E59F7CB7F1D9569">13.1-2 IsWrapperCapCategoryObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X7B2D95DA7D635FD7">13.1-3 IsWrapperCapCategoryMorphism</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap13.html#X7C701DBF7BAE649A">13.2 <span class="Heading">Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X81829E6386E43EF3">13.2-1 UnderlyingCell</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X7AA0358D85F1CD9F">13.2-2 UnderlyingCell</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap13.html#X86EC0F0A78ECBC10">13.3 <span class="Heading">Constructors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X83886A588035ED96">13.3-1 AsObjectInWrapperCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X832CBD5A80B84DDF">13.3-2 AsMorphismInWrapperCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X7A95EED57AD2AF78">13.3-3 AsMorphismInWrapperCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X7BF21C4587D89462">13.3-4 /</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X7C22BC7182777CF4">13.3-5 WrapperCategory</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap13.html#X86932DDE8378A2AF">13.3-6 WrappingFunctor</a></span>
</div></div>
</div>

<h3>13 <span class="Heading">Create wrapper hulls of a category</span></h3>

<p><a id="X7D03633A7D98026B" name="X7D03633A7D98026B"></a></p>

<h4>13.1 <span class="Heading">GAP categories</span></h4>

<p><a id="X82BF68357D8889C4" name="X82BF68357D8889C4"></a></p>

<h5>13.1-1 IsWrapperCapCategory</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsWrapperCapCategory</code>( <var class="Arg">arg</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>The <strong class="pkg">GAP</strong> category of a wrapper CAP category.</p>

<p><a id="X7E59F7CB7F1D9569" name="X7E59F7CB7F1D9569"></a></p>

<h5>13.1-2 IsWrapperCapCategoryObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsWrapperCapCategoryObject</code>( <var class="Arg">arg</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>The <strong class="pkg">GAP</strong> category of objects in a wrapper CAP category.</p>

<p><a id="X7B2D95DA7D635FD7" name="X7B2D95DA7D635FD7"></a></p>

<h5>13.1-3 IsWrapperCapCategoryMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsWrapperCapCategoryMorphism</code>( <var class="Arg">arg</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>The <strong class="pkg">GAP</strong> category of morphisms in a wrapper CAP category.</p>

<p><a id="X7C701DBF7BAE649A" name="X7C701DBF7BAE649A"></a></p>

<h4>13.2 <span class="Heading">Attributes</span></h4>

<p><a id="X81829E6386E43EF3" name="X81829E6386E43EF3"></a></p>

<h5>13.2-1 UnderlyingCell</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; UnderlyingCell</code>( <var class="Arg">object</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a category object</p>

<p>The cell underlying the wrapper category object <var class="Arg">object</var>.</p>

<p><a id="X7AA0358D85F1CD9F" name="X7AA0358D85F1CD9F"></a></p>

<h5>13.2-2 UnderlyingCell</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; UnderlyingCell</code>( <var class="Arg">morphism</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a category morphism</p>

<p>The cell underlying the wrapper category morphism <var class="Arg">morphism</var>.</p>

<p><a id="X86EC0F0A78ECBC10" name="X86EC0F0A78ECBC10"></a></p>

<h4>13.3 <span class="Heading">Constructors</span></h4>

<p><a id="X83886A588035ED96" name="X83886A588035ED96"></a></p>

<h5>13.3-1 AsObjectInWrapperCategory</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; AsObjectInWrapperCategory</code>( <var class="Arg">category</var>, <var class="Arg">object</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: an object</p>

<p>Wrap an object <var class="Arg">object</var> (in the category underlying the wrapper category <var class="Arg">category</var>) to form an object in <var class="Arg">category</var>.</p>

<p><a id="X832CBD5A80B84DDF" name="X832CBD5A80B84DDF"></a></p>

<h5>13.3-2 AsMorphismInWrapperCategory</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; AsMorphismInWrapperCategory</code>( <var class="Arg">source</var>, <var class="Arg">morphism</var>, <var class="Arg">range</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism</p>

<p>Wrap a morphism <var class="Arg">morphism</var> (in the category underlying the wrapper category <code class="code">CapCategory(</code><var class="Arg">source</var><code class="code">)</code>) to form a morphism in <code class="code">CapCategory(</code><var class="Arg">source</var><code class="code">)</code> with given source and range.</p>

<p><a id="X7A95EED57AD2AF78" name="X7A95EED57AD2AF78"></a></p>

<h5>13.3-3 AsMorphismInWrapperCategory</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; AsMorphismInWrapperCategory</code>( <var class="Arg">category</var>, <var class="Arg">morphism</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a morphism</p>

<p>Wrap a morphism <var class="Arg">morphism</var> (in the category underlying the wrapper category <var class="Arg">category</var>) to form a morphism in <var class="Arg">category</var>.</p>

<p><a id="X7BF21C4587D89462" name="X7BF21C4587D89462"></a></p>

<h5>13.3-4 /</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; /</code>( <var class="Arg">cell</var>, <var class="Arg">category</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Convenience method for <code class="func">AsObjectInWrapperCategory</code> (<a href="chap13.html#X83886A588035ED96"><span class="RefLink">13.3-1</span></a>) and <code class="func">AsMorphismInWrapperCategory</code> (<a href="chap13.html#X7A95EED57AD2AF78"><span class="RefLink">13.3-3</span></a>).</p>

<p><a id="X7C22BC7182777CF4" name="X7C22BC7182777CF4"></a></p>

<h5>13.3-5 WrapperCategory</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; WrapperCategory</code>( <var class="Arg">category</var>, <var class="Arg">options</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a category</p>

<p>Wraps a category <var class="Arg">category</var> to form a new category subject to the options given via <var class="Arg">options</var>, which is a record with the following keys:</p>


<ul>
<li><p><code class="code">name</code> (optional): the name of the wrapper category</p>

</li>
<li><p><code class="code">only_primitive_operations</code> (optional, default <code class="code">false</code>): whether to only wrap primitive operations or all operations</p>

</li>
</ul>
<p>Additionally, the following options of <code class="func">CategoryConstructor</code> (<a href="chap11.html#X8070F8B48111E8A7"><span class="RefLink">11.2-1</span></a>) are supported: <code class="code">category_filter</code>, <code class="code">category_object_filter</code>, <code class="code">category_morphism_filter</code>. The filters must imply <code class="code">IsWrapperCapCategory</code>, <code class="code">IsWrapperCapCategoryObject</code>, and <code class="code">IsWrapperCapCategoryMorphism</code>, respectively.</p>

<p><a id="X86932DDE8378A2AF" name="X86932DDE8378A2AF"></a></p>

<h5>13.3-6 WrappingFunctor</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; WrappingFunctor</code>( <var class="Arg">W</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a functor</p>

<p>Return the functor from the wrapped category <code class="code">ModelingCategory</code>(<var class="Arg">W</var>) to the wrapper category <var class="Arg">W</var> which simply wraps objects/morphisms.</p>


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